How Much Money Entering the First Store?

Date: 09/26/2002 at 02:58:00
From: Tim Willock
Subject: Algebra word problem

Timothy spent all of his money at five stores. At each store, he spent 
$1 more than half of the amount he had when entering the store. How 
much money did he have when he entered the first store?

I have tried to create the problem with 1/2X+1 as the first integer, 
but I am stuck and not sure I am even on the right track.  

Thank you for any help you are able to give me.

Tim Willock

Date: 09/26/2002 at 09:24:52
From: Doctor Ian
Subject: Re: Algebra word problem

Hi Tim,

The key to this, I think, is that he spent _all_ of his remaining 
money at the fifth store.  

Let's say he spent $N there. That has to be $1 more than half of what 
he had when he came in. But it also has to be _all_ of what he had 
when he came in.  So 

  N = (N/2) + 1

Once you know what he had going into the fifth store, you can work 
backward to find out what he had going into each of the others.  

Can you take it from here? 
  
- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/